Answer
The voltage of the circuit $E$ in volts is $\left( 47+13i \right)$.
Work Step by Step
Consider the equation, $I=\left( 4-5i \right)$ and $R=\left( 3+7i \right)$
The voltage of the circuit in volts is,
$E=IR$
Substitute $I=\left( 4-5i \right)$ and $R=\left( 3+7i \right)$ in the formula$E=IR$.
$E=\left( 4-5i \right)\left( 3+7i \right)$
Use the FOIL method.
$\begin{align}
& E=4\cdot 3+4\cdot 7i-5i\cdot 3-5i\cdot 7i \\
& =12+28i-15i-35{{i}^{2}} \\
& =12+13i-35{{i}^{2}}
\end{align}$
Replace the value ${{i}^{2}}=-1$.
$\begin{align}
& E=12+13i-35\left( -1 \right) \\
& =12+35+13i \\
& =47+13i
\end{align}$
Therefore, the voltage of the circuit $E$ in volts is $\left( 47+13i \right)$.
